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Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ , the surface tension of water is T and the atmospheric pressure is p o . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

Options

  1. A| 2 p 0 R h + π R 2 ρ g h - 2 R T |
  2. B| 2 p 0 R h + R ρ g h 2 - 2 R T |
  3. C| p 0 π R 2 + R ρ g h 2 - 2 R T |
  4. D| p 0 π R 2 + R ρ g h 2 + 2 R T |

Correct answer

B. | 2 p 0 R h + R ρ g h 2 - 2 R T |

Step-by-step solution

Force from right hand side liquid on left hand side liquid, (i) Due to surface tension force = 2RT (towards right) (ii) Due to liquid pressure force = p 0 + ρ g x 2 R d x = 2 R ρ 0 h + R ρ g h 2 Net force is 2 p o R h + R p g h 2 − 2 R T

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